Computers
are truly amazing machines.They
are marvels of the modern age.They
in fact make the modern age what it is.Without
computers we wouldnot have access to the knowledge and comforts that we now take for
granted. But what, exactly, makes them so
powerful?

The
power of computers rests in their ability to process information for us.The faster they do this, the faster we can solve problems and arrive at
solutions.Computers have improved
over the years and are now so fast that problems and calculations that used to
take many years can be solved in fractions of a second.Because of their amazing success in problem solving, computers have been
integrated into practically every aspect of our lives.Scientists have especially turned to the computer as a tool to
investigate the natural world.In
fact, many feel like the computer can simulate nature itself, even life itself.Scientists have created computer programs that apparently show how life
grows, competes, changes, and of course, evolves.The computer itself has even been compared to a living creature.Many feel that someday computers will arrive at a point of human-like
intelligence and self-awareness.A
world of intelligent silicon-based creatures will co-exist with carbon-based
creatures, both growing and evolving together.
Some suggest that computer human hybrids will also develop.

This
is the stuff of science fiction of course, but many times the science fiction of
the past is the reality of today.Discovering
the very language of life has been a human dream for centuries, and now it is
here.Today we humans are
manipulating the very language that defines our own existence.The coded language of DNA has been cracked and great strides have been
made in reading, understanding, and even manipulating what this language says
and how it is then expressed in living things - even ourselves.In a similar way, humans create and then manipulate the coded languages
of computers.The similarities
between computer language and the language of life are striking.If the language of living things could be fully understood, it seems
reasonable that it could eventually be programmed into computer code.An immortal computer "copy" of it could be created and given
an existence in either a computer animated world or a bio-robotic world.For example, a human might one day exist, with all human functions,
thoughts, feelings, and physical needs, in computer code and animation (much
like the movie, "The Matrix").How
might this be possible?

Computer
function is based on a coded language written using an alphabet of only two
letters called "zero" and "one."The
function of living things is also based on a coded language written using a
chemical alphabet of only four letters labeled "A, T, G, and C."Already the similarity between computers and living things is striking.Everything that we are is written down in a book of sorts.The
writing of this book employs a real alphabet and a real language.So far, the only difference between the genetic code of humans and the
binary code of computers is the difference in the number of letters used.We have four letters while computers have only two letters to work with.The only difference here is that more letters enable greater information
compaction.However, both alphabets
can be set up to code for the same information without any change to the clarity
of that information.As long as the
reader of the information understands the code or language that the alphabet is
written in, the information itself need not be changed.

Since
the basic language or code of life is so similar to the basic language or code
of computer systems, it seems quite logical that one could be used to simulate
the other.In fact, scientists have
recently created DNA computers that actually work based on the four letters in
our own genetic alphabet.Likewise,
scientists have also used computers to simulate organic life, reproduction, and
evolution.Many of these computer
simulations look impressive indeed.But
are these computer animations really growing, changing, or evolving?

In
this line, a recent and very interesting paper was published by Lenski et.
al., entitled, "The Evolutionary Origin of Complex Features" in the
2003 May issue of Nature. In this particular experiment the researchers studied 50 different populations,
or genomes, of 3,600 individuals. Each individual began with 50 lines of code
and no ability to perform "logic operations". Those that evolved the
ability to perform logic operations were rewarded, and the rewards were larger
for operations that were "more complex". After 15,873 generations, 23
of the genomes yielded descendants capable of carrying out the most complex
logic operation: taking two inputs and determining if they are equivalent (the
"EQU" function). The lines of code that made up these individuals
ranged from 49 to 356 instructions long. The ultimately dominant type of
individual contained 83 instructions and the ability to perform all nine logic
functions that allowed it to gain more computer time.

In
principle, 16 mutations (recombinations) coupled with the three instructions
that were present in the original digital ancestor could have combined to
produce an organism that was able to perform the complex equivalence operation.
What actually happened was a bit more complicated. The equivalence operation
function evolved after 51 to 721 steps along the evolutionary path, and the
"organisms" used anywhere from 17 to 43 instructions to carry it out.
The most efficient of the evolved equivalence functions was just 17 lines of
code - two fewer than the most efficient code the researchers had come up with
beforehand. Evolving even as few as 17 lines required a few more than 16
recombination/mutation events (but not that many really, considering that the
majority of these "mutations" were functional). In one case, 27 of the
35 instructions that an organism used to perform the logic operation were
derived through recombination, and all but one of them had appeared in the line
of descent before the complex function was performed.

The
researchers' model involved 103 single mutations/recombinations, six double
mutations, and a pair of triple mutations. In the short-term 45 of those were
beneficial, 48 neutral, and 18 detrimental. Thirteen of the 45 beneficial steps
gave rise to logic functions not expressed by the immediate parent. Fifteen of
the 18 detrimental mutations made the offspring slightly less fit, or likely to
propagate, than the parent. Two of the detrimental mutations cut in half the
offspring's fitness. One of these very detrimental mutations, however, did
produce offspring that one step later produced a mutation that in turn gave rise
to the complex logic operation.

This
all looks very much like the evolution of complex software functions in computer
code and many are quite convinced that the parallel is very close to what
happens in the natural world. However, there are several interesting
constraints to this experiment. For one thing, the ultimate functional goal was
predetermined as with Dawkins's "Methinks it is like a weasel"
computer evolution experiment - except that there was a difference here in that
each of the steps involved with Lenski's experiment were actually functionally
unique. The problem is that these functions were predetermined by intelligent
design to be functionally beneficial. Basically, the proper environment was a
set-up for the success of a particular evolutionary scenario, which was already
pre-determined via intelligent design. Also, the types of mutations that
were used were not generally point mutations, but were based on swapping large
sections of pre-programmed meaningful bit code around. The researchers knew that
with a relatively few recombinations of code such a logic function of
"increasing complexity" would be realized. After all, the environment
was set up to produce changes were the ratio of beneficial changes as compared
to all other potential changes was very high. Like the evolution of antibiotic
resistance this function was easy to evolve given the restraints used by the
scientists because the neutral gaps were set up to be so small. Also, the
success of the experiment was dependent on pre-established lines of code that
were set up to work together to solve logical problems of a specific type.

I
suggest however that this particular setup would not be able to evolve other
types of functions, like the ability to open the CD-drive or the ability to
cause the monitor to blink off and on. The gaps involved would require different
types of starting code sequences that could not be gained by the type of code
recombination used in this experiment. Point mutations would be required
and very large gaps in function would need to be crossed before these other
functions could be realized.

In
short, I think that this experiment was a setup for the success of a very
limited goal and does not explain the evolution of uniquely functional systems
beyond the most elementary of levels. It did end up producing some
"unexpected" solutions to the problem, but that is only to be
expected. There might be many different ways to interfere with an antibiotic's
interaction with a target sequence that might not be otherwise expected.
However, the functional ratio is what is important here and clearly it is very
high as compared to the neutral sequences (40% beneficial mutations vs. 10%
detrimental and only 43% neutral - Please! Give me a break!). Success was
guaranteed by the way the intelligent designers set up their experiment.
They were able to sequentially define their own environment ahead of time in a
very specified way. The logic functions that were evolved were dependent
upon the proper selective environment being set up ahead of time by ID. What if
there was a gap between one type of logic function and another type of logic
function? - such as between the NAND and the EQU functions that required the
evolution of either the AND or the OR, or the NOR, XOR or NOT functions first?
What if these functions were not recognized by a particular environment as being
beneficial? Then, there would be a neutral gap created by that environment
between the NAND and EQU functions. What are the odds that the
"proper" environment that recognized at least one of these other
functions as beneficial, would come around at the right time?

You
see, the random walk not only includes random changes in code, but also in
environment. Without an intelligent mind directing changes in environment in
just the proper way, the organic synthesis of many different compounds that are
made in chemistry laboratories would not work. The order of the environmental
changes is just as important as the order of the molecules in the
"evolution" of new functions or compounds.

Interestingly
enough, Lenski and the other scientists thought of this potentiality themselves,
so they set up different environments to see which environements would support
the evolution of all the potentially beneficial functions - to include the most
complex EQU function. Consider the following description about what
happened when various intermediate steps were not arbitrarily defined by the
scientists as "beneficial".

"At
the other extreme, 50 populations evolved in an environment where only EQU was
rewarded, and no simpler function yielded energy. We expected that EQU would
evolve much less often because selection would not preserve the simpler
functions that provide foundations to build more complex features. Indeed,
none of these populations evolved EQU, a highly significant difference from
the fraction that did so in the reward-all environment (P = 4.3 x 10e-9,
Fisher's exact test). However, these populations tested more genotypes, on
average, than did those in the reward-all environment (2.15 x 10e7 versus 1.22
x 107; P<0.0001, Mann-Witney test), because they tended to have smaller
genomes, faster generations, and thus turn over more quickly. However, all
populations explored only a tiny fraction of the total genotypic space. Given
the ancestral genome of length 50 and 26 possible instructions at each site,
there are ~5.6 x 10e70 genotypes; and even this number underestimates the
genotypic space because length evolves."

Isn't
that just fascinating? When the intermediate stepping stone functions were
removed, the neutral gap that was created successfully blocked the evolution of
the EQU function. Now, isn't this consistent with my predictions? This
experiment was successful because the intelligent designers were capable to
defining what sequences or functions were "beneficial" for their
evolving "organisms." If enough sequences or functions are defined as
beneficial, then certainly such a high ratio will result in rapid evolution - as
we saw here. However, when neutral non-defined gaps are present, they are a real
problem for evolution. In this case, a gap of just 16 neutral mutations
effectively blocked the evolution of the EQU function. (Just for those who are
curious, listed with the references are the detailed "Experimental
Conditions" listed by the authors).

The
problem here is that without the input of higher information from the
intelligent minds of the scientists, this experiment would have failed.
All specified systems of function of increasing complexity require the input of
some sort of higher pre-established source of information - be that information
stored in the form of a genetic code or a human scientist. The reason for
this is that left to themselves, the individual parts simply do not know how to
arrange themselves in any particular orientation with other parts to create a
specified function of high complexity. Because of this, the best that the
parts themselves can self-assemble, without the aid of a higher source of
information, is a homogenous ooze or a homogenous crystalline structure.

Many
people think that all changes in function are equal - that just any example of
evolution in action can explain all other differences in function. The
fact is that there are different levels of functional complexity. Some
changes are much easier to achieve than others. But all
change costs something. This price is called "entropy."
The entropy of a system is a description of that system's ability to do useful
work. In other words, it is a description of non-equilibrium or
non-homogeny. For example, consider two boxes A and B. Both boxes
contain gas molecules. The molecules in box B are hotter and therefore
move faster. If allowed to mix, the disequilibrium creates a gradient that
can be used to perform useful work. For example, the motion of the gas
from box B to box A could be used to turn a fan and create electrical energy.
However, when equilibrium is reached, the fan will no longer turn. At
equilibrium, the entropy of this system is said to be at it's maximum.
Statistically, it is possible for the gas molecules, by some random chance
coincidence, to happen to bounce around just right so that they all end up back
in box B, turning the fan as they go. This is in fact possible, but is it
probable? Entropy is therefore a description of work probability. A
drop of water from a fishbowl might organize its molecular energy so that it
stands up and walks right out of the fish bowl and jumps down onto the table
below. This event is statistically possible but it is very improbable that
the molecules in that particular drop of water would just happen to act together
in such a fashion - according to the laws of entropy.

So,
according to the law of entropy, all mindless natural changes tend toward
equilibrium - or the lowest state of probable work potential. How then do
living things seem to buck the system? Living systems strive to maintain
disequilibrium or a low state of entropy. Living systems move and work
constantly without loosing the ability to work. In fact they often
increase their ability to work the more that they work. Does this not go
directly against a fundamental law of nature? It would seems that they do
except for the fact that the work done by living things comes at an entropic
cost to the surrounding environment or "system." The entropy of
the universe increases every time you scratch your ear or blink your eyes.
However, when a living thing dies, it no longer maintains itself in
disequilibrium. It can no longer buck the law of entropy. The
building blocks of the living system immediately begin to fall back into
equilibrium with each other to form a homogenous ooze. Living systems are
fairly unique in that they are consistently able to take this same homogenized
ooze and use it to form nonhomogenized systems capable of work. How do
living systems do this? They are programmed to do this with a pre-existing
code of information much like computers are programmed to buck entropy.

Computers
create non-homogeny just like living systems do. They create order out of
apparent chaos. They can be programmed to organize disordered
(homogenized) building blocks so that they will have a working function.
Of course there are many different types of workable systems that could be
created given a particular set of building blocks. The same building
blocks could be used to build a house or a car. Computers do not know this
however. They are programmed to use the building blocks to build only what
they are told to build. The same is true for living systems. Living
things build only what their DNA tells them to build. The fact is that the
same basic building blocks are used in all living things, but the individual
cell only knows what its DNA tells it. Once specialized, a single cell in
the toe of a turtle only knows how to use the building blocks to make turtle toe
parts. The question of course is, can computers or living things build ordered
systems that go uniquely beyond or outside of their original programming?

No
one questions the idea that change happens.Change is obvious. However, can a mindless natural law process that
always tends toward equilibrium end up working against itself by contributing to
the establishment of new and unique ways of reducing equilibrium? Is there
any known natural law process that would upgrade a computer's software and or
hardware outside of intelligent human creativity? We do know that the
genetic make-up (software) of all creatures does in fact "change."The "software" programs of living things do in fact change. How
does this happen?These changes are
surprisingly not part of the software package itself.These changes are apparent accidents.They are not based on the normal functions of life, but in the normal
functions of natural law.These
natural law changes are referred to as "random mutations" in the
software of living things.If
allowed to continue unchecked, these mutations tend toward non-functional
homogeny.By themselves, these
mutations can in fact increase the specified order or functional complexity of
the software package - but only in the most limited way. In the same way a
few molecules of water in a river may run uphill for a while, but not for very
long and not in any significant way.Why
is this?Because they follow the
natural law of entropy. Mutations in any
system generally tend toward random homogeny, disorder, nonfunction, or an
inability to work. Rarely one or two mutations may happen to come
across a new and beneficial function of increasing complexity - but always these
new functions are from the lowest levels of functional complexity. For
example, although very simple functions like antibiotic resistance and even the
evolution of unique single protein enzymes (like the lactase or nylonase
enzymes) have been shown to evolve in real time, no function on the higher level
of a multi-protein system where each protein works together at the same time in
a specified orientation to the other proteins has been observed to evolve.
Such multi-protein part systems are everywhere, to include such systems as
bacterial motility systems (like the flagellum) and yet not one of them has been
observed to evolve - period.Just
like the drop of water walking out of the fish bowl, it is statistically
possible for hypermutation to create new and amazing systems of function of very
high complexity, but it just never happens beyond the lowest levels of
functional complexity. Hypermutation follows the laws of increasing
entropy just like the gas molecules in boxes A and B until equilibrium is
reached. Death is the ultimate end of hypermutation. No living thing
can tolerate hypermutation for very long.

But, natural
selection is supposed to come to the rescue - but does it?Natural selection is a process where nature selects those software
changes that produce more durable and reproducible hardware given a
particular environment and discards the ones that do not.In this way, the random mutations that would otherwise lead to homogeny
are manipulated by the guiding force of natural selection toward a diversity of
functions that go farther and still farther away from homogeny.Natural selection is supposed to be an amazing power.It is supposed to be able to subvert a fundamental law of nature by
turning meaningless non-working, non-functional, homogenous ooze into more and
still more diversely working systems.How
does natural selection do this?Natural
selection is said to rely on statistical probability.For example, lets say that only one out of a million random software
changes or mutations is beneficial.If
this benefit is detectable by nature, or any other selecting force, then things
can be improved over time.The
statistics of random chance, when combined with a selective force, are bent in
favor of higher order instead of disorder.The question then arises, if natural selection works so well for the
improvement of the software of living things, then why not use it to improve
computer software as well?This
question does seem reasonable since both kinds of systems us a similar coded
language.If natural selection
works with one alphabet, it should just as easily be able to work with the other
alphabet.And yet, this has not
happened with either computers or the "software" of living things
beyond the lowest levels of functional complexity.Why not?

It
turns out that natural selection cannot read the coded
language of computers or living things.Natural selection does not see the alphabets of either system.Natural selection is only capable of selecting hardware changes or
changes in hardware function. But isn't
hardware function based in the software and wouldn't changes to the software
change hardware function? Yes and no. Hardware function is
completely based in the software, but this basis is dependent upon a specified
arrangement of parts. Not all arrangements will have the same function,
much less any beneficial function at all. Sometimes the functional meaning
of a particular part is quite arbitrary - just as the meaning of a word is
arbitrarily attached to a series of symbols called letters. Without this
arbitrary attachment, the letters themselves mean nothing and have no function.
The same is true for bit and bytes in a computer and for the genetic code in
living things. So, if the symbols change or get mutated to something that
does not have a meaning or a function arbitrarily attached to them, then there
is no recognized function. There is no expressed phenotype. Without
a phenotype, they are invisible to the process of natural selection. All
subsequent changes to their underlying code are "neutral" and from
here on out are dependent upon laws of random chance alone. This always
leads to lifeless homogeny. So, what are the odds that random chance will
buck the law of increasing entropy and "work"? What are the odds
that the drop of water will dance out of the fish bowl?

Still
not convinced? Lets take a closer look into the languages of computers and
living things. Computer language
is set up using a system of "bits" and "bytes."A bit is either a zero or a one.Eight
bits in a series is a byte.For
example, the series 10101010 is a byte.If
a bit is comparable to a letter in the English language, then a byte is
comparable to a word.The computer
assigns various meanings to the "byte words."This assignment of meaning or function is arbitrary, as it is in any
symbolic language (and as it was with the Lenski experiment where various
functions were arbitrarily defined as being "beneficial").The same thing happens with genetic words in living systems.Therefore, a single byte could be assigned an alphanumeric "meaning"
such as the letter "A."For a
series of eight bits, there are 256 different possible combinations.This means that a computer byte could represent up to 256 separate
defined functions.Each of these
words would have to have a separate recognized definition in the computer's
arbitrary dictionary of words.

The
same is true for any living system.Every
genetic word in DNA has an arbitrary definition assigned to it by the "genetic
code."However, instead ofthere being eight letters per defined word, the genetic code only
recognizes three-letter words called "codons." 1Since there are four genetic letters in DNA instead of only two in
computer language, there could be up to 64 different defined codons in the
genetic code.In reality, the
genetic code gives several codons the same definition so that there is some
redundancy, but it does in fact have the capacity to recognize up to 64
different definitions.

So,
if a computer’s code gave a separate functional definition to each one of 256
possible bytes in its dictionary, a single change in any given byte would yield
a detectable change in function.If
this change was a desired change, it could be kept while other changes could be
discarded.Evolution would be a
simple and relatively quick process.The
problem is that a computer needs more than 256 separate functions and even the
simplest living system needs far more than 64 separate functions.How are these needs met?What
if multiple words are used to code for other unique definitions?What if two bytes were joined together and given a completely unique
definition by the computer?How
many possible functions would there be now?There would be 65,536 different possible defined functions that could be
recognized in the computer’s dictionary.

This
is in fact what happens.Computer
codes assign arbitrary meaning to multiple bytes.Likewise, the DNA language of living systems is translated into another
language of living systems called proteins.The protein language is based on an alphabet of 20 letters called amino
acids.1A protein is put
together in linear order as dictated by a linear codon sequence in the DNA.This protein can be very long, hundreds or even thousands of amino acid
"letters" long and yet it is assigned an arbitrary meaning by the
particular system that it "fits" in with.Because of the vast number of possible proteins of a given length, not
every protein has a defined or beneficial function in a given life form or
system of function as it acts in a particular environment.
Of course, this means that not every change in DNA and therefore protein
sequencing will result in a beneficial change in system function.The same is true for computers.Because
of the combination of defined bytes in computer language, some of the possible
bytes or byte combinations will not be defined as "beneficial".If these happen to “evolve” by random mutation, they will not yield a
change up the ladder of functional complexity.

To
illustrate this point consider that in living systems each of 64 codons code for
one of only 20 amino acids. We can
now draw a parallel and imagine a computer where the 256 bytes each code for one
of the 26 letters of the English alphabet, a space, and a period to make only 28
possible characters.Now, lets
imagine a computer that defines functions according to English words or phrases
averaging 28 characters in length.How
many different functional definitions would be available to this computer?The answer is quite huge at 3 x 1040.To help one understand this number, the human genome contains only about
35,000 genes.2That
means that to create a completely functional human, it takes less than 35,000
uniquely defined proteins.This is
on the very small side of what is possible for recognized proteins.If a given function required just one protein averaging only 100 amino
acids in length there would be 1 x 10130 different potential proteins
that could be used (That is a 1 with 130 zeros after it).However, human "systems" only recognize the smallest fraction out of
all these possibilities.The same
is true for computer systems.

Lets
say then that our computer recognizes 1,000,000 separate written commands of a
level of function that averages 28 English characters in length.Starting with one recognized command, how long would it take to "evolve" any other recognized command at that level of function if a unique
command was tried each and every second?You
see the initial problem?It is one
of recognition.If the one
recognized word is changed, it will no longer be recognized.It will be functionless.Without
recognized function, there is no guidance or driving force in any future word
changes.The changes from here on
out are strictly dependent upon random chance alone (so called "neutral" evolution).The
statistics of random walk say that on average it would take 3 x 1026
years or one hundred trillion trillion years to arrive at another word that is
recognized or "functional."Without
a functional pathway each and every step of the way, this neutral gap blocks the
power of natural selection to select and therefore this gap blocks the change of
one beneficial phrase into any other beneficial phrase of a particular level of
complexity.

So
far, computers have not been able to evolve their own software beyond the most
simple levels of function (as described above) without the help of intelligent
design from computer scientists.Computers
are always dependent upon outside programming for any changes in function
that go up the ladder of complexity beyond the lowest levels of functional
complexity.A computer, as of
today, cannot evolve brand new software programs or do much of anything beyond
its original programming.Why?Because, if the selector can only select based on function, then, as one
moves up the ladder of functional complexity, the selector will soon be blinded
by gaps of neutral changes in the underlying code which give the selector no
clue that the changes have even taken place much less which changes are
"better" or "worse" than any other "neutral"
change.

I
propose that the same problems hold true when it comes to Darwinian-style
evolution in living things.Nature
can only select based on what it sees.What
nature sees is function - not the underlying language code or molecular symbols
in the DNA itself.The statistical
gaps between the recognized words in a living system’s dictionary are huge.
The gaps are so huge that, to date, the best evolutionary evidence
demonstrated in the lab describes changes separated by only one, two or possibly
three amino acid "letter" changes.3Without experiments or good statistical arguments to explain these
problems, evolutionary theories are in serious trouble when they try to explain
the existence of complex computer or biological functions that rise above the
lowest rungs on the ladder of specified functional complexity.

1.Gelehrter, Thomas D. et al. Principles
of Medical Genetics, 1998.

2.Lemonick, M. Gene Mapper,
Time, Vol. 156, No. 26, pp110, 2001.

3.B.G. Hall, Evolution on a Petri Dish.The Evolved B-Galactosidase System as a Model for Studying Acquisitive
Evolution in the Laboratory, Evolutionary Biology, 15(1982): 85-150.

"Avida
software was used. Every population started with 3,600 identical copies of
an ancestral genotype that could replicate but could not perform any logic
functions. Each replicate population that evolved in the same environment
was seeded with a different random number. The hand-written ancestral genome
was 50 instructions long, of which 15 were required for efficient
self-replication; the other 35 were tandem copies of a single no-operation
instruction (nop-C) that performed no function when executed. Copy errors
caused point mutations, in which an existing instruction was replaced by any
other (all with equal probability), at a rate of 0.0025 errors per
instruction copied. Single-instruction deletions and insertions also
occurred, each with a probability of 0.05 per genome copied. Hence, in the
ancestral genome of length 50, 0.225 mutations are expected, on average, per
replication. Various organisms from nature have genomic mutation rates
higher or lower than this value. Mutations in Avida also occasionally cause
the asymmetrical division of copied genome, leading to the deletion or
duplication of multiple instructions. Each digital organism obtained
'energy' in the form of SIPs at a relative rate (standardized by the total
demand of all organisms in the population) equal to the product of its
genome length and computational merit, where the latter is the product of
rewards for logic functions performed. The exponential reward structure
shown was used in the reward-all environments, whereas some functions
obtained no reward under other regimes. An organism's expected reproductive
rate, or fitness, equals its rate of energy acquisition divided by the
amount of energy needed to reproduce. Fitness can also be decomposed into
replication efficiency (ratio of genome length to energy required for
replication) and computational merit. Each population evolved for 100,000
updates, an arbitrary time unit equal to the execution of 30 instructions,
on average, per organism. The ancestor used 189 SIPs to produce an
offspring, so each run lasted for 15,873 ancestral generations. Populations
existed on a lattice with a capacity of 3,600 individuals. When an organism
copied its genome and divided, the resulting offspring was randomly placed
in one of the eight adjacent cells or in the parent's cell. Each birth
caused the death of the individual that was replaced, thus maintaining a
constant population size."